Question

solve the following pairs of linear equations by reducing them to linear equations 2/x + 3/y = 13 and 5/x - 4/y = - 2​

Answer 1

let 1/x=u and 1/y=v

then, 2u+3v=13........(i)

5u-4v=-2

using elimnation method

multiplying (i) by 4 and (ii) by 3

8u+12v=52

15u-12v=-6

----------------

23u=46

u=2

putting value of u in (i)

2*2+3v=13

3v=13-4

3v=9

v=3

now,1/x=2

2x=1

•x=1/2

again,1/y=3

3y=1

•y=1/3

Answer 2

Solution:-

Given Linear Equations;

2/x + 3/y = 13 and 5/x - 4/y = - 2

Let ( 1/x = u ) and ( 1/ y = v)

=) 2u + 3v = 13__________(1)

&

=) 5u - 4v = -2.__________(2)

By Elimination Method!

Multiplying Eq (1) by 4 and Eq (2) by 3. we get,

=) 8u + 12v = 52

=) 15u - 12v = -6

_______________

=) 23u. = 46

=) u = 46/23

=) u = 2.

Putting ( u =2) in Eq. (2). we get,

=) 5×2 - 4v = -2

=) -4v = -2 -10

=) v = 12/4

=) v = 3.

According to our Supposition,

1/x = u = 2

=) x = 1/2

& 1/y = v = 3

=) y = 1/3.

Hence Solved!